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HUA-TYPE ITERATION FOR MULTIDIMENSIONAL WEYL SUMS

Part of: Additive number theory; partitions Exponential sums and character sums Diophantine equations

Published online by Cambridge University Press:  27 March 2012

Scott T. Parsell
Scott T. Parsell*
Affiliation:
Department of Mathematics, West Chester University, 25 University Ave., West Chester, PA 19383, U.S.A. (email: sparsell@wcupa.edu)
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Abstract

We develop Weyl differencing and Hua-type lemmata for a class of multidimensional exponential sums. We then apply our estimates to bound the number of variables required to establish an asymptotic formula for the number of solutions of a system of diophantine equations arising from the study of linear spaces on hypersurfaces. For small values of the degree and dimension, our results are superior to those stemming from the author’s earlier work on Vinogradov’s mean value theorem.

MSC classification

Secondary: 11D45: Counting solutions of Diophantine equations 11D72: Equations in many variables 11L07: Estimates on exponential sums 11L15: Weyl sums 11P55: Applications of the Hardy-Littlewood method

Information

Type
Research Article
Information
Mathematika , Volume 58 , Issue 2 , July 2012 , pp. 209 - 224
Copyright
Copyright © University College London 2012

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